| In current CFD,the numerical simulation of unsteady flow remains a challenge.The main difficulty for solving unsteady flow problems stems from the fact that practical numerical scheme is required to be second-order time-accurate.The widely used dual-time-step scheme nowadays could be in theory second-order accuracy with respect to time.But when used in 3D viscous flow simulations,the scheme might become inefficiency as the number of subiteration increases.On the other hand,if the efficiency is improved by limiting the number of subiterations,the time accuracy of the method will be deteriorated.Such,the efficiency and the time accuracy of the existing numerical algorithms still needs to be improved before numerical simulations of unsteady three dimensional viscous flow become practical day-to-day engineering tools.On the other hand,in some unsteady flow simulations,the high quality dynamic grid becomes a necessity for accurate computation of flow solutions.However,the grid generation methods we used may not provide automatic means of preserving grid orthogonality and smoothness,or they are very computationally time-consuming and suffer from numerical inefficiency.Such the method which can generate high quality dynamic grids and overcome the computational inefficiency has been a subject of continuing importance.The work of the dissertation is as follows.First,a hybrid explicit-implicit scheme was developed by combining the explicit Runge-Kutta with implicit LU-SGS.The method based on the finite volume solves the nonstiff portions of the computational domain using explicit Runge-Kutta method,and solves the stiff portions using implicit dual time stepping method.In general,the proportion of steep gradients in flow field will not be large,so a significant reduction of the implicit equations and computer storage can be achieved.To implement the scheme,a method called “j-direction splitting” is developed,where the blocks of the grid may only be split in explicit and implicit domain along the direction of steep gradient.On the basis of the work above,the paper presents another hybrid explicit-implicit scheme combining explicit RK with implicit DTS which is time-accurate and has second order accuracy with respect to time.The main idea is the same as used in the method of Runge-Kutta+LU-SGS.The difference is the choice of physical time step size and the division of geometric region.In the time-accurate scheme,both the stability limit on the time step size and the requirement of time accuracy have to be considered.Thus,used here is a method which chooses the minimum of the maximum allowable time steps for all explicit blocks as the unified global physical time step.And some suggestions have been made as to how to split the grid in order to alleviate the time step.In a word,the numerical results show that the hybrid explicit-implicit schemes preposed in the paper are stable and convergent for the validation case.The advantages of the schemes are:(1)the computer memory storage required at each time step decreases considerablely because of a significant reduction of the implicit equations in the system matrix of discretised governing equation;(2)a substantial number of subiterations can be avoid in the explicit portions,this makes the time-accurate scheme more efficient and practical for the solution of complex unsteady flows.Furthermore,a simple robust structured dynamic grid generation method based on the solution of elliptic partial differential equations is developed for computing the unsteady flows with moving boundaries.In the method,the source terms of the elliptic equation which control the spacing and the orthogonality of the grid are inherited from the known static grid,and held fixed throughout the procedure of dynamic grid generation.With the procedure,the outer iterations for determining the source terms usually needed in the elliptic grid generation can be saved.No adjustable parameters are required to be prescribed.This makes the method more efficient and easy to implement in an existing CFD code. |
